q-LMF: Quantum Calculus-based Least Mean Fourth Algorithm
This work addresses channel estimation for communication systems, offering an incremental improvement over existing adaptive learning methods.
The paper tackles channel estimation in non-Gaussian noisy environments by proposing the q-LMF algorithm, an extension of the least mean fourth method based on q-calculus, which achieves significant performance gains in convergence rate, stability, and steady-state error compared to contemporary techniques.
Channel estimation is an essential part of modern communication systems as it enhances the overall performance of the system. In recent past a variety of adaptive learning methods have been designed to enhance the robustness and convergence speed of the learning process. However, the need for an optimal technique is still there. Herein, for non-Gaussian noisy environment we propose a new class of stochastic gradient algorithm for channel identification. The proposed $q$-least mean fourth ($q$-LMF) is an extension of least mean fourth (LMF) algorithm and it is based on the $q$-calculus which is also known as Jackson derivative. The proposed algorithm utilizes a novel concept of error-correlation energy and normalization of signal to ensure high convergence rate, better stability and low steady-state error. Contrary to the conventional LMF, the proposed method has more freedom for large step-sizes. Extensive experiments show significant gain in the performance of the proposed $q$-LMF algorithm in comparison to the contemporary techniques.